In a multi-antenna communication system, multiple (NT) transmit antennas and one or more (NR) receive antennas are typically used for data transmission. The NT transmit antennas may be used to increase system throughput by transmitting different data from the antennas or to improve reliability by transmitting data redundantly. In the multi-antenna communication system, a propagation path exists between each pair of transmit and receive antennas. NT·NR different propagation paths are formed between the NT transmit antennas and the NR receive antennas. These propagation paths may experience different channel conditions (e.g., different fading, multipath, and interference effects) and may achieve different signal-to-noise-and-interference ratios (SNRs). The channel responses of the NT·NR propagation paths may thus vary from path to path, and may further vary over time for a time-variant wireless channel and across frequency for a dispersive wireless channel. The variant nature of the propagation paths makes it challenging to transmit data in an efficient and reliable manner.
Accordingly, one way to improve reliability for data transmission is to employ transmit diversity with a beamformer, which can potentially improve a link budget by more than three decibels (3 dB). For example, transmit diversity generally refers to redundant transmission of data across space, frequency, time, or a combination thereof. Among other things, transmit diversity may be used to maximize diversity for the data transmission across as many dimensions as possible to achieve robust performance and to simplify the processing for transmit diversity at both a transmitter and a receiver. Another complementary technique that can be used to improve performance of wireless transmissions is to employ beamforming to control the directionality of the transmitted signal. In transmitting systems or devices, beamforming may be employed between a signal source and antenna radiating elements to “shape” a radiated field in three dimensional space towards the receiving system(s) or device(s). In order to steer the beam toward the receiving system(s) or device(s), the transmitting system or device needs an estimate of the radio channel. However, existing techniques to obtain the channel estimate for a particular link between two devices assume that the channel is invariant and reciprocal, which often cannot be guaranteed in a wireless personal area network (WPAN) in which devices communicate using a frequency hopping scheme.